Shortest path planning in discretized workspaces using dominance relation

Various forms of shortest path planning (SPP) have been studied by numerous researchers. Although SPP is generally regarded as a solved problem in 2D space, few of the existing 2D solutions can be applied to 3D. Since many real-world applications are based on 3D or higher space, this deficiency severely limits the applicability of 2D solutions. In this paper, we present a new method of partitioning the workspace using rectilinear visibility in 3D or higher space. Unlike the case of 2D space where the shape of a partition is a rectangle, the shape of a partition in 3D or higher space is arbitrary. However, we can prove the existence of dominance relations between the partitioned regions. This relation is then utilized to efficiently solve the SPP problem in 3D or higher space. Key Words-Find path problem, L , and L, metrics, path planning, rectilinear visibility, shortest-path planning, visibility graph.